1、Designation: E 511 01Standard Test Method forMeasuring Heat Flux Using a Copper-Constantan CircularFoil, Heat-Flux Transducer1This standard is issued under the fixed designation E 511; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision
2、, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method describes the measurement of radiativeor convective heat flux, or both, using a transd
3、ucer whosesensing element (1, 2)2is a thin circular metal foil. Whilebenchmark calibration standards exist for radiative environ-ments, no uniform agreement among practitioners or govern-ment entities exists for convective environments.1.2 The values stated in SI units are to be regarded as thestand
4、ard. The values stated in parentheses are provided forinformation only.1.3 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine th
5、e applica-bility of regulatory limitations prior to use.2. Summary of Test Method2.1 The purpose of this test method is to facilitate measure-ment of heat flux from radiant or convective sources, or froma combination of the two.2.2 The circular foil heat flux transducer generates a milli-volt output
6、 in response to the rate of thermal energy absorbed(see Fig. 1). The circular metal foil sensing element is mountedin a metal heat sink around its perimeter, forming a referencethermocouple junction due to their different thermoelectricpotentials. A second thermocouple junction is formed at thecente
7、r of the foil using a fine wire of the same metal as the heatsink. When the sensing element is exposed to a heat source,heat energy is absorbed at the surface of the circular foil andconducted radially to the heat sink. This establishes a parabolictemperature gradient between the center and edge of
8、the foil.The temperature gradient produces a thermoelectric potential,E, between the center wire and the heat sink that will vary inproportion to the heat flux, q9. With prescribed foil diameter,thickness, and materials, the potential E is linearly proportionalto the heat flux q9 absorbed by the foi
9、l. This relationship isdescribed by the following equation:E 5 Kq9where:K = a sensitivity constant determined experimentally.2.3 For linear response, the heat sink of the transducernormally is made of copper and the foil of thermocouple gradeconstantan. This combination of materials produces a linea
10、routput over a temperature range from -45 to 232C (-50 to450F). The linear range results from offsetting effects oftemperature-dependent changes in the thermal conductivityand Seebeck coefficient of the constantan. All further discus-sion is based on the use of these two metals, since engineeringpra
11、ctice has demonstrated they are commonly the most useful.3. Characteristics and Limitations3.1 The principal response characteristics of a circular foilheat flux transducer are sensitivity, full-scale range, and thetime constant, which are established by the foil diameter andthickness. For a given h
12、eat flux, the transducer sensitivity isproportional to the temperature difference between the centerand edge of the circular foil. To increase sensitivity, the foil ismade thinner or its diameter is increased. The full-scale rangeof a transducer is limited by the maximum allowed temperatureat the ce
13、nter of the foil. The range may be increased by makingthe foil smaller in diameter, or thicker. The transducer timeconstant approximately is proportional to the square of the foildiameter, and is characterized by (3):t5rcd2/16kwhere the foil properties are:r = density,c = specific heat,d = foil diam
14、eter, andk = foil conductivity.3.2 Foil diameters and thicknesses are limited by typicalmanufacturing constraints. Maximum optimum foil diameter tothickness ratio is 4 to 1 for sensors less than 2.54 mm diameter.Foil diameters range from 25.4 mm to 0.254 mm, with mostgages between 1.02 and 6.35 mm.
15、The time constants, t, for a25.4-mm and 0.254-mm diameter foil are 6 s and 0.001 s,respectively. For constantan, the time constant is approximated1This test method is under the jurisdiction of ASTM Committee E21 on SpaceSimulation and Applications of Space Technology and is the direct responsibility
16、 ofSubcommittee E21.08 on Thermal Protection.Current edition approved Oct. 10, 2001. Published January 2002. Originallypublished as E 511 73. Last previous edition E 511 73 (1994)e1.2The boldface numbers in parentheses refer to the list of references at the end ofthis test method.1Copyright ASTM Int
17、ernational, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.by t = 0.0094 d2, where d is in mm.3.3 The sensitivity of commercially available transducers islimited to about 2 mV/W/cm2(1.76 BTU/ft2/s). Higher sensi-tivities can be achieved, but the foils of more sen
18、sitivetransducers are extremely fragile. The range of commercialtransducers may be up to 10 000 W/cm2(8811 BTU/ft2/s), andtypically is limited by the capacity of the heat sink for heatremoval. The full-scale range is normally specified as thatwhich produces 10 mV of output. This is the potentialprod
19、uced by a copper-constantan transducer with a temperaturedifference between the foil center and edge of 190C (374F).These transducers may be used to measure heat fluxes exceed-ing the full-scale (10 mV output) rating; however, more than50 % over-ranging will shorten the life and possibly change thet
20、ransducer characteristics. If a transducer is used beyond 200 %of its full-scale rating, it should be returned to the manufacturerfor inspection and recalibration before further use. Care shouldbe taken not to exceed recommended temperature limits toensure linear response. This is designed for in tw
21、o ways: activecooling and by providing a heatsink with the copper body.Water-cooled sensors should be used in any application inwhich the sensor body would otherwise rise above 235C(450F). Typical cooled assemblies are shown in Fig. 2. Whenapplying a liquid-cooled transducer in a hot environment, it
22、may be important to insulate the body of the transducer fromthe surrounding structure if it is also hot. This will improve theeffectiveness of cooling and reduce the required liquid flowrate.3.4 The temperature of the gage normally is low in com-parison to the heat source. The resulting heat flux me
23、asured bythe gage is known as a “cold wall” heat flux. For measurementof purely radiant heat flux, the circular foil is coated with ablack paint or carbon soot of high absorptivity (0.98) Since thetransducer signal is a direct response of the energy absorbed bythe foil, the absorptivity of the surfa
24、ce of the coating must beknown to correctly calculate the incident radiation flux.3.5 Error Sources3.5.1 Physical or chemical processes other than heat transfermay affect the accuracy of measurements made with a circularfoil heat-flux transducer. If the dew point of the atmosphere atthe face of the
25、transducer is above the temperature of thecircular foil, condensation may occur. This will release heatenergy sensed as heat flux resulting in errors; thus, it isadvisable to use a cooling water supply whose temperature isabove the dew point of the atmosphere surrounding thetransducer. Measurements
26、of heat flux produced by flames inclosed chambers are particularly subject to this error if the fuelbeing burned contains hydrogen. Catalytic processes at the faceof the transducer (4) can cause similar errors.3.5.2 A circular foil transducer can be used in a vacuum forradiant heat flux measurements
27、, but if maximum accuracy isdesired, the transducer should be calibrated in a similarvacuum. The output of the transducer will be slightly higher ina vacuum because of a small convective heat flow between theback of the foil and the body of the transducer when it is usedFIG. 1 Heat DrainEither by Wa
28、ter Cooling the Body with a Surrounding Water Jacket or Conducting the Heat Away with SufficientThermal MassE5112at atmospheric pressure, to a degree that depends on the foildimensions.3.5.3 The circular foil transducer cannot be used for con-ducted heat-flux measurements.3.5.4 Commercial transducer
29、s are calibrated with heat fluxsources that are essentially uniform over the foil area, produc-ing a parabolic temperature difference across the foil. If atransducer is used to measure a sharply focused light source,such as a laser beam or imaging optical system, its calibrationmay not be valid.3.5.
30、5 The field of view of a circular foil transducer used forradiative heat flux measurements is a half plane, or 180.Transducer sensitivity to a point source of heat flux is greatestat normal incidence, and follows an approximate cosine law forother angles. Off-normal radiative sensitivity may be a fu
31、nctionof the incident wavelength and the condition of the circular foilsurface. Measurements made with a circular foil transducer andany other transducer (for example, radiometer) with a morelimited field of view are not directly comparable unless theradiant source for both transducers has uniform i
32、ntensity overthe 180 field of view.3.6 Convection3.6.1 Circular foil transducers may be used to measureconvective heat transfer, but certain cautions (5, 6, 7) should beobserved. Because the heat transfer due to convection isproportional to the difference in temperature in the normaldirection betwee
33、n the fluid and the surface, the gradient intemperature along the foil in the parallel direction creates anonuniform heat flux. This nonuniformity is maximized whenthe bulk flow is parallel to the surface (8). The nonuniformityis lessened when the full-scale range of the transducer is muchgreater th
34、an the expected maximum convective heat flux, sothe temperature rise at the center of the foil is closer to that ofits edge. A method for selecting the transducer full-scale rating(9) has been developed, but its utility is limited by therequirement that the convective heat transfer coefficient mustb
35、e known. Generally, the transducer should produce no morethan 0.5 mV output at the maximum convective heat flux, or a10C (18F) temperature difference from foil center to edge.Under these circumstances, electrical noise may limit thesignal resolution.4. Description of the Instrument4.1 Fig. 1 is a se
36、ctional view of an example circular foilheat-flux transducer. It consists of a circular foil attached by ametallic bonding process to a heat sink of oxygen-free highconductivity copper (OFHC), with copper leads attached at thecenter of the circular foil and at any point on the body. Thisdata acquisi
37、tion system (DAS) should be potentiometric, orhave an input impedance of at least 100 000 ohms. Thetransducer impedance is usually less than 1 ohm.4.2 A linear output (versus heat flux) is produced when thebody and center wire of the transducer are constructed ofcopper and the circular foil is const
38、antan. Other metal combi-nations may be employed for use at higher temperatures, butmost (10) are nonlinear.4.3 Because the thermocouple at the edge of the foil is thereference for the center thermocouple, no cold junction com-pensation is required with this instrument. The wire leads usedto convey
39、the signal from the transducer to the readout deviceare normally made of stranded, tinned copper, insulated withTFE-fluorocarbon and shielded with a braid over-wrap that isalso TFE-fluorocarbon-covered.4.4 Transducers with a heatsink thermocouple can be usedto indicate the foil center temperature. T
40、he temperature differ-ence from the foil edge to its center may be directly read fromthe copper-constantan (Type T) thermocouple table. Thistemperature difference then is added to the body temperature,indicating the foil center temperature. The effects of foildimensions on transducer characteristics
41、 are shown in Figs. 3and 4.4.5 Water-Cooled Transducer4.5.1 A water-cooled transducer should be used in anyapplication where the copper heatsink would rise above 235C(450F) without cooling. Examples of cooled transducers areshown in Fig. 2. The coolant flow must be sufficient to preventFIG. 2 Cross-
42、Sectional View of Water-Cooled Heat-Flux GagesE5113local boiling of the coolant inside the transducer body, with itscharacteristic pulsations (“chugging”) of the exit flow indicat-ing that boiling is occurring. Water-cooled transducers can usebrass water tubes and sides for better machinability andm
43、echanical strength.4.5.2 The water pressure required for a given transducerdesign and heat-flux level depends on the flow resistance andthe shape of the internal passages. Rarely will a transducerrequire more than a few litres of water per min. Most requireonly a fraction of L/min.4.5.3 Heat fluxes
44、in excess of 3405 W/cm2(3000 Btu/ft2/s)may require transducers with thin internal shells for efficienttransfer of heat from the foil/heat sink into a high-velocitywater channel. Velocities of 15 to 30 m/s (49 to 98 ft/s) areproduced by water at 3.4 to 6.9 MPa (500 to 1000 psi). Forsuch thin shells,
45、zirconium-copper may be used for its combi-nation of strength and high thermal conductivity.4.6 Foil Coating4.6.1 Thin coatings of metallic and nonmetallic materials onthe circular foil may be used to modify the transducerperformance/response to radiative or convective heat sources.For example, the
46、absorptance of the foil surface may beincreased or decreased by a coating of paint or reflective metal.High-absorptance coatings are used when radiant energy is tobe measured. Ideally, the high-absorptance coating shouldprovide a nearly diffuse absorbing surface, where absorption isindependent of th
47、e angle of incidence of radiation on thecoating. An ideal coating also would have no dependency ofabsorption with wavelength, approximating a gray-body. Onlya few coatings approach these ideal characteristics.4.6.2 Acetylene soot (total absorptance aT= 0.99) and cam-phor soot (aT= 0.98) have the dis
48、advantages (10) of lowoxidation resistance and poor adhesion to the transducersurface. Colloidal graphite coatings dried from acetone oralcohol solutions (aT= 0.83) are commonly used because theyadhere well to the transducer surface over a wide temperaturerange. Spray black lacquer paints (aT= 0.94
49、to 0.98), some ofwhich may require baking, also are used. They are intermediatein oxidation resistance and adhesion between the colloidalgraphites and soots. Colloidal graphite is commonly used as aprimer for other, higher-absorptance coatings.4.6.3 Low-absorptance metallic coatings, such as highlypolished gold or nickel, may be used to reduce a transducersresponse to radiant heat. Because these coatings effectivelyincrease the foil thickness, they reduce the transducer sensitiv-ity. Gold coating also makes the transducer response nonlinearbecause the thermal conductivity
